Calculating Sled Speed on a Frictionless Hill: Equations for Theta and Radius

[mookie84]

Homework Statement

A sled starts from rest at the top of the frictionless, hemispherical hill. What is the equation to calculate the sleds speed at angle (theta)

Homework Equations

The Attempt at a Solution

I need to figure out the equation. I'm given theta and the radius. I thought the equation was Rsin(theta) but that was incorrect

 

[hotcommodity]

We're told that the hill is frictionless, so we can use the conservation of mechanical energy to find the sleds speed at some angle theta. After finding the final speed, you'll want to use Newton's Second Law along with the equation for centripetal acceleration to find the sleds speed at some angle theta. Can you show me how you would set up the equation for the conservation of mechanical energy?